TWI781509B - System and method for transforming sparse elements into a dense matrix, and non-transitory machine-readable storage device - Google Patents

Abstract

Methods, systems, and apparatus, including a system for transforming sparse elements to a dense matrix. The system is configured to receive a request for an output matrix based on sparse elements including sparse elements associated with a first dense matrix and sparse elements associated with a second dense matrix; obtain the sparse elements associated with the first dense matrix fetched by a first group of sparse element access units; obtain the sparse elements associated with the second dense matrix fetched by a second group of sparse element access units; and transform the sparse elements associated with the first dense matrix and the sparse elements associated with the second dense matrix to generate the output dense matrix that includes the sparse elements associated with the first dense matrix and the sparse elements associated with the second dense matrix.

Description

System and method for transforming sparse elements into a dense matrix, and non-transitory machine-readable storage

This description generally relates to the use of circuits to process a matrix.

According to one novel aspect of the subject matter set forth in this specification, a matrix processor can be used to perform a sparse-to-dense or a dense-to-sparse matrix transformation. In general, a HPC system can use linear algebra formulas to process a matrix. In some instances, the size of the matrix may be too large to fit in one data store, and different parts of the matrix may be stored sparsely in different locations in a distributed data storage system. To load the matrix, the central processing unit of a computing system can instruct a separate circuit to access different parts of the matrix. The circuitry may include memory controllers configured according to a network topology, wherein sparse data may be partitioned and stored based on a predetermined set of rules. Each memory controller can aggregate sparse data based on the predetermined set of rules to perform concurrent computations on the sparse data and generate a dense matrix that can be chained together for further processing by the central processing unit. In general, a novel aspect of the subject matter set forth in this specification can be embodied in a system for transforming sparse elements into a dense matrix. The system includes: a first group of sparse element access units configured to retrieve sparse elements associated with a first dense matrix; and a second group of sparse element access units configured to Extract the first dense moment with The sparse elements associated with a second dense matrix of arrays. The system is configured to: receive a request for an output matrix based on sparse elements including sparse elements associated with a first dense matrix and sparse elements associated with a second dense matrix; obtain the sparse elements associated with the first dense matrix extracted from the first sparse element access unit group; obtaining the sparse elements associated with the second dense matrix extracted from the second sparse element access unit group the sparse elements; and transforming the sparse elements associated with the first dense matrix and the sparse elements associated with the second dense matrix to generate the sparse elements associated with the first dense matrix and the output dense matrix of the sparse elements associated with the second dense matrix. These and other implementations can each optionally include one or more of the following features. For example, the first sparse element access unit group may include a first sparse element access unit and a second sparse element access unit. The first sparse element access unit can be configured to retrieve a first subset of the sparse elements associated with the first dense matrix. The second sparse element access unit can be configured to retrieve a second different subset of the sparse elements associated with the first dense matrix. The first sparse element access unit is configured to receive a request for a plurality of sparse elements including the sparse elements associated with the first dense matrix and the sparse elements associated with the second dense matrix ; and transmitting the request to the second sparse element access unit. The first sparse element access unit may be configured to determine an identity of a particular sparse element of the plurality of sparse elements and one of the first subset of the sparse elements associated with the first dense matrix One of the sparse elements identity matches. The first sparse element access unit may be configured in response to determining the identity of the particular sparse element of the plurality of sparse elements and the first subset of the sparse elements associated with the first dense matrix The identity of a sparse element is matched to extract the first subset of the sparse elements associated with the first dense matrix including the particular sparse element. The first sparse element access unit can be configured to retrieve the first subset of the sparse elements associated with the first dense matrix from a first data partition, and the second sparse element access unit can configured to extract the second different subset of the sparse elements associated with the first dense matrix from a second different data partition. The first sparse element access unit may be configured to transform the first subset of the sparse elements associated with the first dense matrix to produce a third dense matrix, and the second sparse element access unit can be configured to receive the third dense matrix; transform the second subset of the sparse elements associated with the second dense matrix to produce a fourth dense matrix; and transform the third dense matrix with the first Quad dense matrix to produce a fifth dense comprising the first subset of the sparse elements associated with the first dense matrix and the second subset of the sparse elements associated with the first dense matrix matrix. The first sparse element access unit group and the second sparse element access unit group may be configured in a two-dimensional mesh configuration. The first sparse element access unit group and the second sparse element access unit group may be configured in a two-dimensional torus configuration. The sparse elements associated with the first dense matrix and the sparse elements associated with the second dense matrix may be multidimensional matrices, and the output dense matrix may be a vector. The subject matter set forth in this specification can be implemented in particular embodiments so as to realize one or more of the following advantages. Connecting the memory controller units according to a network topology allows partitioning the storage of sparse data following a predetermined set of rules. Offloading the sparse to dense data loading task from the central processing unit to a separate circuit increases the computational bandwidth of the central processing unit and reduces the processing cost of the system. By using dedicated circuitry, the use of processors dedicated to dense linear algebra to extract sparse data can be avoided. By using multiple memories simultaneously in a distributed system, the aggregate aggregate bandwidth available in a distributed system is higher than that required for a single memory bank that needs to be serialized and has a single memory capacity with respect to the aggregate bandwidth . Other implementations of this and other aspects include corresponding systems, apparatus, and computer programs encoded on computer storage devices configured to perform the actions of the methods. A system of one or more computers may be so configured by means of software, firmware, hardware or a combination thereof installed on the system which in operation causes the system to perform actions. One or more computer programs may be so configured by having instructions that when executed by a data processing device cause the device to perform actions. Details of one or more implementations of the subject matter set forth in this specification are set forth in the accompanying drawings and the description below. Other possible features, aspects and advantages of the subject matter will be clarified according to the description, drawings and scope of patent application.

Generally, data can be represented in the form of a matrix and a computing system can manipulate the data using linear algebra algorithms. A matrix can be a one-dimensional vector or a multidimensional matrix. A matrix can be represented by a data structure such as a database table or a variable. However, when the size of a matrix is too large, it may not be possible to store the entire matrix in a data store. A dense matrix can be transformed into a plurality of sparse elements, where each sparse element can be stored in a different data store. A sparse element of a dense matrix may be a matrix in which only a small submatrix (eg, a single-valued element, column, row, or submatrix) of the matrix has nonzero values. When a computing system needs to access the dense matrix, the central processing unit (CPU) can start going to each of the data stores to fetch a thread of stored sparse elements, and apply a sparse-dense transformation to restore the dense matrix. However, the amount of time it takes to fetch all sparse elements can be significant, and it turns out that the computational bandwidth of the CPU can be underutilized. In some cases, a computing system may need to access sparse elements of several dense matrices, where the dense matrices may not be of equal size, to form a new dense matrix. The CPU idle time associated with a thread reaching each of the data stores to fetch the sparse elements of the different dense matrices may suffer from different latencies and may further affect the performance of the computing device in an undesirable manner. In some cases, a computing system may need to access sparse elements of several dense matrices, where the sparse elements may not be of equal size, to form a new dense matrix. The CPU idle time associated with a thread reaching each of the data stores to fetch the sparse elements of the different dense matrices may suffer from different latencies and may further affect the performance of the computing device in an undesirable manner. A hardware sparse-to-dense transformation unit separate from a CPU can increase the computational bandwidth of the processor by collecting sparse elements and transforming the sparse elements into a dense matrix operating independently of the CPU. 1 shows a block diagram of an example computing system 100 for transforming sparse elements from one or more dense matrices to produce a dense matrix. The computing system 100 includes a processing unit 102 , a sparse-dense transformation unit 104 and data partitions 106 a to 106 k , wherein k is an integer greater than 1. In general, the processing unit 102 processes an instruction for accessing a target dense matrix, and sends an instruction 110 to the sparse-dense transformation unit 104 to generate the target dense matrix. The sparse-to-dense transformation unit 104 accesses corresponding sparse elements 108 a to 108 n from one or more of the data partitions 106 a to 106 k , where n is an integer greater than one. The sparse-to-dense transformation unit 104 generates the target dense matrix 112 using the corresponding sparse elements 108a-108n, and provides the target dense matrix 112 to the processing unit 102 for further processing. For example, the sparse elements 108a-108n may be two-dimensional matrices with different sizes, and the sparse-dense transformation unit 104 may convert each of the sparse elements 108a-108n into a vector and concatenate the n vectors into a single vector to produce the target dense matrix 112. In certain implementations, the processing unit 102 may process an instruction to update a target dense matrix and send an updated dense matrix to the sparse-dense transform unit 104 . The sparse-dense transformation unit 104 may transform the updated dense matrix into corresponding sparse elements and accordingly update one or more sparse elements stored in the data partitions 106a-106k. Processing unit 102 is configured to process instructions for execution within computing system 100 . The processing unit 102 may include one or more processors. In some implementations, the processing unit 102 is configured to process the target dense matrix 112 generated by the sparse-to-dense transform unit 104 . In certain other implementations, the processing unit 102 may be configured to request the sparse-dense transformation unit 104 to generate the target dense matrix 112 , and another processing unit may be configured to process the target dense matrix 112 . Data partitions 106a-106k store data including sparse elements 108a-108n. In some implementations, the data partitions 106a-106k may be one or several volatile memory units. In some other implementations, the data partitions 106a-106k may be one or several non-volatile memory units. Data partitions 106a-106k may also be another form of computer-readable medium, such as a device in a storage area network or other configuration. Data partitions 106a-106k may be coupled to sparse-dense transformation unit 104 using electrical, optical, or wireless connections. In certain implementations, the data partitions 106 a - 106 k may be part of the sparse-to-dense transform unit 104 . The sparse-to-dense transformation unit 104 is configured to determine a dense matrix based on sparse elements. In some implementations, the sparse-dense transformation unit 104 can be configured to determine the locations of sparse elements based on a dense matrix. In certain implementations, the sparse-to-dense transform unit 104 may include a plurality of interconnected sparse element access units, as explained in more detail below with reference to FIGS. 2A-2D . FIG. 2A shows an example sparse-dense transform unit 200 . The sparse-dense transform unit 200 may correspond to the sparse-dense transform unit 104 . The sparse-dense transformation unit 200 includes M × N sparse element access units X _1,1 to X _M,N physically or logically arranged in M columns and N rows, where M and N are integers equal to or greater than 1 . In certain implementations, the sparse-to-dense transform unit 200 may include additional circuitry configured to process data. In general, the sparse-to-dense transformation unit 200 is configured to receive a request for a dense matrix and determine a dense matrix based on corresponding sparse elements accessible by sparse element access units X _1,1 through X _M,N matrix. In general, each sparse element access unit is configured to access a specified set of sparse elements, and is explained in more detail below with reference to FIGS. 3A-3B . In some implementations, a sparse element access unit may be a single instruction multiple data (SIMD) processing device. In some embodiments, the sparse element access units X _1,1 to X _M,N can be physically or logically configured in a two-dimensional mesh configuration. For example, sparse element access unit X _1,1 is directly coupled to sparse element access units X _1,2 and X _2,1 . As another example, sparse element access unit X _2,2 is directly coupled to sparse element access units X _2,1 , X _3,1 , X _2,3 and X _1,2 . The coupling between two sparse element access units may be an electrical connection, an optical connection, a wireless connection, or any other suitable connection. In some other embodiments, the sparse element access units X _1,1 to X _M,N may be physically or logically configured in a two-dimensional torus configuration. For example, sparse element access unit X _1,1 is directly coupled to sparse element access units X _1,2 , X _2,1 , X _1,N and X _M,1 . As another example, the sparse element access unit X _M,N is directly coupled to the sparse element access units X _M,N-1 , X _M-1,N , X _M,1 and X _1,N . In some implementations, the sparse-to-dense transform unit 200 may be configured to partition the sparse elements transformed from the dense matrix according to a predetermined set of conditions. Each column of sparse element access units X _1,1 to X _M,N can be partitioned to access sparse elements from a particular dense matrix transformation. For example, the sparse-dense transformation unit 200 can be configured to access sparse elements from dense matrix transformations corresponding to 1,000 different database tables of a computer model. One or more of the database tables may be of different sizes. The first column 202 of the sparse element access unit can be configured to access sparse elements converted from database table No. 1 to database table No. 100, and the second column 204 of the sparse element access unit can be configured to store Sparse elements from database table 101 transformed to database table 300, and row M of the sparse element access unit 206 can be configured to access data transformed from database table 751 to database table 1,000 sparse elements. In some implementations, partitioning may be configured by hardware instructions before a processor uses the sparse-to-dense transform unit 200 to access sparse elements. Each row of sparse element access units X _1,1 to X _M,N can be partitioned to access a subset of sparse elements from a particular dense matrix transformation. For example, the dense matrix corresponding to database table number 1 can be transformed into 1,000 sparse elements, where the 1,000 sparse elements can be accessed by the first column 202, as explained above. Sparse element access unit X _1,1 can be configured to access sparse elements No. 1 to No. 200 of database table No. 1, and sparse element access unit X _1,2 can be configured to access data No. 1 Sparse elements from No. 201 to No. 500 of the library table. As another example, the dense matrix corresponding to database table No. 2 can be transformed into 500 sparse elements, where the 500 sparse elements can be accessed by the first column 202, as set forth above. Sparse element access unit X _1,1 can be configured to access sparse elements No. 1 to No. 50 of database table No. 2, and sparse element access unit X _1,2 can be configured to access data No. 2 Sparse elements No. 51 to No. 200 of the library table. As another example, a dense matrix corresponding to database table number 1,000 can be transformed into 10,000 sparse elements, where the 10,000 sparse elements can be accessed by the Mth column 206, as set forth above. Sparse element access unit X _M,1 can be configured to access sparse elements No. 1 to No. 2,000 of database table No. 1,000, and sparse element access unit X _{M, N} can be configured to access data No. 1,000 9,000 to 10,000 sparse elements of the library table. FIG. 2B shows an example of how the sparse-to-dense transformation unit 200 may request sparse elements using a two-dimensional mesh of sparse element access units. As an example, a processing unit may execute an instruction to request the sparse-dense transformation unit 200 for one of the following: using sparse elements No. 1 to No. 50 of database table No. Elements and sparse elements 9,050 to 9,060 of the 1,000 database table yield a dense one-dimensional vector. After sparse-dense transformation unit 200 receives a request from a processing unit, sparse-dense transformation unit 200 may instruct sparse element access unit X _1,1 to broadcast a request for a sparse element to other sparse elements in the mesh network access unit. Sparse element access unit X _1,1 may broadcast a request 222 to sparse element access unit X _1,2 and a request 224 to sparse element access unit X _2,1 . After receiving the request 222, the sparse element access unit X _1,2 may broadcast a request 226 to the sparse element access unit X _1,3 . In some implementations, a sparse element access unit can be configured to broadcast a request to another sparse element access unit based on a routing scheme. For example, sparse element access unit X _1,2 may not be configured to broadcast a request to sparse element access unit X _2,2 because sparse element access unit X _2,2 is configured to receive Broadcast from one of the sparse element access units X _2,1 . The routing scheme can be static or dynamically generated. For example, the routing scheme can be a lookup table. In certain implementations, one sparse element access unit can be configured to broadcast a request 224 to another sparse element access unit based on the request 224 . For example, request 224 may include an identification of the requested sparse element (e.g., database table number 1, sparse element numbers 1 through 50), and based on these identifications, sparse element access unit X _1,2 may determine whether The request 224 is broadcast to the sparse element access unit X _2,2 and/or the sparse element access unit X _1,3 . The broadcast procedure is propagated through the mesh network, wherein the sparse element access unit XM, _N receives a request 230 from the sparse element access unit _XM,N−1 . FIG. 2C shows an example of how the sparse-to-dense transform unit 200 may generate a requested dense matrix using a two-dimensional mesh network of sparse element access units. In some implementations, after a sparse element access unit receives a broadcast request, the sparse element access unit is configured to determine whether it is configured to access any of the requested sparse elements. For example, sparse element access unit X _1,1 may determine that it is configured to access sparse elements 1 through 50 of database table 1, but it is not configured to access database table 2 100 to 200 sparse elements or 9,050 to 9,060 sparse elements of 1,000 database tables. In response to determining that it is configured to access sparse elements 1 through 50 of tables of database 1, sparse element access unit X _1,1 may fetch database 1 from the data partition in which these sparse elements are stored Sparse elements No. 1 to No. 50 of the table, and generate a dense matrix 242 based on these sparse elements. As another example, sparse element access unit X _2,1 may determine that it is not configured to access sparse elements 1 through 50 of database table 1, and sparse elements 100 through 200 of database table 2. element or any of the sparse elements 9,050 to 9,060 of the 1,000 database table. In response to determining that it is not configured to access any of the requested sparse elements, sparse element access unit X _2,1 may not perform any further action. As another example, sparse element access unit X _1,2 may determine that it is configured to access sparse elements 100 through 200 of table 2 in database 2, but it is not configured to access database 1 Sparse elements 1 to 50 for tables or 9,050 to 9,060 for database tables 1,000. In response to determining that it is configured to access sparse elements 100 through 200 of database table 2, the sparse element access unit X _1,2 may fetch these sparse elements from the data partition in which they are stored , and a dense matrix 244 is generated based on these sparse elements. In some implementations, after a sparse element access unit generates a dense matrix, the sparse element access unit may be configured to forward the dense matrix to the sender of the broadcast request. Here, the sparse element access unit X _1,2 forwards the dense matrix 244 to the sparse element access unit X _1,1 . As another example, sparse element access unit _XM,N may determine that it is configured to access sparse elements 9,050 to 9,060 of table 1,000, but it is not configured to access database 1 Sparse elements No. 1 to No. 50 of the table or No. 100 to No. 200 sparse elements of the No. 2 database table. In response to determining that it is configured to access sparse elements 9,050 through 9,060 of database table 1,000, the sparse element access unit XM _,N may extract these sparse elements from the data partition in which they are stored , and a dense matrix 246 is generated based on these sparse elements. In some implementations, after a sparse element access unit generates a dense matrix, the sparse element access unit may be configured to forward the dense matrix to the sender of the broadcast request. Here, the sparse element access unit X _M,N forwards the dense matrix 246 to the sparse element access unit X _M,N−1 . In the next cycle, sparse element access unit _XM,N-1 is configured to forward dense matrix 246 to sparse element access unit _XM,N-2 . This procedure continues until sparse element access unit X _2,1 has forwarded dense matrix 246 to sparse element access unit X _1,1 . In certain implementations, the sparse-to-dense transform unit 200 is configured to transform a dense matrix produced by a sparse element access unit and produce a dense matrix for a processor unit. Here, the sparse-to-dense transform unit 200 transforms the dense matrices 242, 244, and 246 into one dense matrix for the processor unit. For example, dense matrix 242 may have dimensions of 100×10, dense matrix 244 may have dimensions of 20×100, and dense matrix 246 may have dimensions of 3×3. Sparse-dense transform unit 200 may transform dense matrices 242, 244, and 246 into one vector having a size of 1x3009. Advantageously, partitioning the columns according to the dense matrix (eg, database table) allows the sparse-dense transformation unit 200 to obtain all the requested sparse elements after the resulting dense matrix has been propagated to row 1 by itself N. Row partitioning reduces bandwidth bottlenecks caused by accessing too many sparse elements using only one of the sparse element access units. FIG. 2D shows an example of how the sparse-to-dense transformation unit 200 may update sparse elements based on a dense matrix using a two-dimensional mesh network of sparse element access units. As an example, a processing unit may execute an instruction that requests the sparse-to-dense transformation unit 200 to update the stored sparse elements with a dense one-dimensional vector using sparse elements 1 through 50 of database table 1 and 9,050 to 9,060 sparse elements of the 1,000 database table. After the sparse-dense transformation unit 200 receives the request from the processing unit, the sparse-dense transformation unit 200 can instruct the sparse element access unit X _1,1 to broadcast a sparse element update request to other sparse element accesses in the mesh network unit, wherein the sparse element update request may include a dense one-dimensional vector provided by the processing unit. In some implementations, the sparse element access unit X _1,1 may determine whether it is assigned to access sparse elements contained in a dense one-dimensional vector. In response to determining that it is assigned to access a sparse element contained in a dense one-dimensional vector, the sparse element access unit X _1,1 may update the sparse element stored in the data partition. Here, sparse element access unit X _1,1 determines that it is assigned to access sparse elements No. 1 to No. 50 of database table No. 1, and sparse element access unit X _1,1 executes update One of such sparse element directives. Sparse element access unit X _1,1 may broadcast a sparse element update request 252 to sparse element access unit X _1,2 and a sparse element update request 254 to sparse element access unit X _2,1 . After receiving the sparse element update request 252, the sparse element access unit X _1,2 may determine that it is not assigned to access the sparse elements contained in the dense one-dimensional vector. The sparse element access unit X _1,2 broadcasts a request 256 to the sparse element access unit X _1,3 . The broadcast procedure is propagated through the mesh network, wherein the sparse element access unit XM, _N receives a request 260 from the sparse element access unit _XM,N−1 . Here, sparse element access unit _XM,N determines that it is assigned to access sparse element numbers 9,050 to 9,060 of database table number 1,000, and sparse element access unit XM _,N executes to update the data partition Instructions for one of these sparse elements. FIG. 3A shows an example sparse element access unit 300 . The sparse element access unit 300 may be any one of the sparse element access units X _1,1 to X _M,N . In general, the sparse element access unit 300 is configured to receive a request 342 from the node network 320 to extract sparse elements stored in one or more data partitions and to transform the extracted sparse elements into a dense matrix. In some embodiments, a processing unit 316 sends a request for a dense matrix generated using sparse elements to a sparse element access unit in node network 320 . The sparse element access unit may broadcast a request 342 to the sparse element access unit 300 . The routing of broadcast request 342 may be similar to that illustrated in FIG. 2B. The sparse element access unit 300 includes a request identification unit 302 , a data extraction unit 304 , a sparse reduction unit 306 , a concatenation unit 308 , a compression/decompression unit 310 and a splitting unit 312 . The node network 320 can be a two-dimensional mesh network. Processing unit 316 may be similar to processing unit 102 . In general, the request identification unit 302 is configured to receive a request 342 to fetch a sparse element stored in one or more data partitions 330, and determine whether the sparse element access unit 300 is assigned to access the sparse element indicated by the request 342 sparse elements. In some implementations, request identification unit 302 may determine whether sparse element access unit 300 is assigned to access the sparse element indicated by request 342 by using a lookup table. For example, if an identification of a particular requested sparse element (e.g., number 1 of database table number 1) is included in the lookup table, request identification unit 302 may extract signal 344 of the particular requested sparse element Send to the data extraction unit 304. If an identification of a particular requested sparse element (eg, number 1 of database table number 1 ) is not included in the lookup table, request identification unit 302 may discard the received request. In certain implementations, the request identification unit 302 may be configured to broadcast the received request to another sparse element access unit on the node network 320 . Data extraction unit 304 is configured to extract one or more requested sparse elements from data partition 330 in response to receiving signal 344 . In some embodiments, the data extraction unit 304 includes one or more processors 322a to 322k, where k is an integer. Processors 322a-322k may be vector processing units (VPUs), array processing units, or any suitable processing units. In some implementations, the processors 322a - 322k are configured near the data partition 330 to reduce latency between the processors 322a - 322k and the data partition 330 . Based on the number of requested sparse elements that sparse element access unit 300 is assigned to fetch, data fetch unit 304 may be configured to generate one or more requests to be distributed among processors 322a-322k. In certain implementations, each of the processors 322a through 322k can be assigned to a particular sparse element based on the identification of the sparse element, and the data extraction unit 304 can be configured to target the processor 322a based on the identification of the sparse element. to 322k to generate one or more requests. In some implementations, the data extraction unit 304 can determine the processor assignment by using a lookup table. In some embodiments, data extraction unit 304 may generate multiple batches for processors 322a through 322k, where each batch is a request for one of a subset of the requested sparse elements. Processors 322 a - 322 k are configured to independently extract assigned sparse elements from data partition 330 , and forward extracted sparse elements 346 to sparse reduction unit 306 . Sparse reduction unit 306 is configured to reduce the size of extracted sparse elements 346 . For example, each of processors 322a-322k may generate a sparse element having a size of 100x1. The sparse reduction unit 306 may receive the extracted sparse elements 346 having a size of 100× k , and generate a result by reducing the size of the extracted sparse elements 346 to 100×1 through logical operations, arithmetic operations, or a combination of both. Sparse reduced elements 348. Sparse downscale unit 306 is configured to output the sparsely downscaled elements 348 to concatenation unit 308 . Concatenation unit 308 is configured to reconfigure and concatenate sparsely reduced elements 348 to produce concatenated elements 350 . For example, the sparse element access unit X _1,1 can be configured to access sparse elements No. 1 to No. 200 of database table No. 1 . The processor 322a may return the extracted sparse element No. 10 to the sparse reduction unit 306 faster than the processor 322b is configured to return the extracted sparse element No. 5. The concatenation unit 308 is configured to reconfigure the later received sparse element No. 5 to be arranged in front of the earlier received sparse element No. 10, and to concatenate the sparse elements Nos. 1 to 200 into the concatenated element 350 . Compression/decompression unit 310 is configured to compress concatenated elements 350 to produce a dense matrix 352 for node network 320 . For example, compression/decompression unit 310 may be configured to compress zero values in concatenated elements 350 to improve the bandwidth of node network 320 . In some implementations, compression/decompression unit 310 may decompress a received dense matrix. For example, sparse element access unit 300 may receive a dense matrix from a neighboring sparse element access unit via node network 320 . Sparse element access unit 300 may decompress the received dense matrix, and may concatenate the decompressed dense matrix with concatenated elements 350 to form updated concatenated elements that may be compressed and then output to node network 320 . FIG. 3B shows an example of how sparse element access unit 300 may update sparse elements based on a dense matrix received from node network 320 . As an example, a processing unit may execute an instruction that requests the sparse-to-dense transformation unit to update the stored sparse elements with a dense one-dimensional vector using sparse elements 1 through 50 of database table 1 and Sparse elements 9,050 to 9,060 of the 1,000 database table are generated. After the sparse-dense transformation unit receives the request from the processing unit, the sparse-dense transformation unit may send one of the following requests 362 instructing the sparse element access unit 300 to determine whether it is assigned to access the sparse elements contained in the dense one-dimensional vector element. The request identification unit 302 is configured to determine whether the sparse element access unit 300 is assigned to access sparse elements contained in a dense one-dimensional vector. In response to determining that the sparse element access unit 300 is assigned to access the sparse elements contained in the dense one-dimensional vector, the request identification unit 302 may send an indication 364 to the split unit 312 to update the sparse elements stored in the data partition. Splitting unit 312 is configured to transform a received dense matrix into sparse elements that can be updated by data extraction unit 304 in data partition 330 . For example, split unit 312 may be configured to transform a dense one-dimensional vector into a plurality of sparse elements, and instruct data fetch unit 304 to update the sparse elements stored in data partition 330 that sparse element access unit 300 is assigned to fetch . FIG. 4 illustrates a flowchart of an example of a procedure 400 for generating a dense matrix. The procedure 400 may be performed by a system such as the sparse-dense transformation unit 104 or the sparse-dense transformation unit 200 . The system may include a first sparse element access unit group and a second sparse element access unit group. For example, referring to FIG. 2A , the sparse-dense transform unit 200 may include M × N sparse element access units X _1,1 to X _M,N physically or logically arranged in M columns and N rows. Each column of sparse element access units X _1,1 to X _M,N can be partitioned to access sparse elements from a particular dense matrix transformation. In some implementations, the first sparse element access unit group may include a first sparse element access unit and a second sparse element access unit. For example, the first column of the sparse-dense transform unit 200 may include sparse element access units X _1,1 and X _1,2 . In some embodiments, the first sparse element access unit group and the second sparse element access unit group may be configured in a two-dimensional mesh configuration. In some implementations, the first sparse element access unit group and the second sparse element access unit group may be configured in a two-dimensional torus configuration. The system receives a request for an output matrix based on sparse elements, including sparse elements associated with a first dense matrix and sparse elements associated with a second dense matrix (402). For example, referring to FIG. 2B, a processing unit may execute an instruction requesting a dense one-dimensional vector from the sparse-dense transformation unit 200, and the dense one-dimensional vector uses the sparse elements No. 1 to No. 50 of the No. 1 database table, The 100th to 200th sparse elements of the No. 2 database table and the 9,050 to 9,060th sparse elements of the 1,000th database table are generated. In some implementations, the first sparse element access unit can receive a request for one of a plurality of sparse elements including a sparse element associated with the first dense matrix and a sparse element associated with the second dense matrix. The first sparse element access unit may transmit the request to the second sparse element access unit. For example, referring to FIG. 2B , after the sparse-dense transformation unit 200 receives the request from the processing unit, the sparse-dense transformation unit 200 may instruct the sparse element access unit X _1,1 to broadcast a request for one of the sparse elements to the network Other sparse element access units in the mesh network. The sparse element access unit X _1,1 may broadcast a request 222 to the sparse element access unit X _1,2 . The system obtains sparse elements associated with the first dense matrix extracted from a first sparse element access unit group (404). In some embodiments, the first sparse element access unit may determine an identity of a particular one of the plurality of sparse elements and a sparse element in a first subset of sparse elements associated with the first dense matrix One of the identities matches. For example, referring to FIG. 2C , the sparse element access unit X _1,1 can be configured to access sparse elements No. 1 to No. 200 of database table No. 1 . Sparse element access unit X _1,1 can determine that it is configured to access sparse elements 1 to 50 of database table 1, but it is not configured to access 100 to 50 of database table 2 200 sparse elements or 9,050 to 9,060 sparse elements of 1,000 database tables. In response to determining that the identity of a particular sparse element of the plurality of sparse elements matches an identity of a sparse element in a first subset of sparse elements associated with the first dense matrix, the first sparse element access unit may extract a sparse element containing the specified A first subset of sparse elements associated with the first dense matrix of sparse elements. For example, in response to determining that it is configured to access sparse elements 1 through 50 of database table 1, the sparse element access unit X _1,1 may be fetched from the data partition in which these sparse elements are stored Sparse elements from No. 1 to No. 50 in No. 1 database table. The second sparse element access unit can fetch a second different subset of the sparse elements associated with the first dense matrix. For example, referring to FIG. 2C , the sparse element access unit X _1,2 can be configured to access sparse elements No. 51 to No. 200 of database table No. 2 . In response to determining that it is configured to access sparse elements 100 through 200 of database table 2, the sparse element access unit X _1,2 may fetch these sparse elements from the data partition in which they are stored . The system obtains sparse elements associated with the second dense matrix extracted from a second sparse element access unit group (406). For example, referring to FIG. 2C, the second sparse element access unit group may be the Mth column of M × N sparse element access units, where the sparse element access unit _XM,N may be configured to access 9,000 to 10,000 sparse elements of 1,000 database tables. In response to determining that it is configured to access sparse elements 9,050 through 9,060 of database table 1,000, the sparse element access unit XM _,N may extract these sparse elements from the data partition in which they are stored , and a dense matrix 246 is generated based on these sparse elements. In some implementations, a first sparse element access unit can extract a first subset of sparse elements associated with a first dense matrix from a first data partition, and a second sparse element access unit can extract a first subset of sparse elements from a first data partition. Two different data partitions extract a second different subset of sparse elements associated with the first dense matrix. For example, referring to FIG. 1, a first sparse element access unit may extract a first subset of sparse elements associated with a first dense matrix from data partition 106a, and a second sparse element access unit may extract from data partition 106b A second distinct subset of sparse elements associated with the first dense matrix is extracted. The system transforms the sparse elements associated with the first dense matrix and the sparse elements associated with the second dense matrix to produce an output comprising the sparse elements associated with the first dense matrix and the sparse elements associated with the second dense matrix Dense Matrix (408). For example, referring to FIG. 2C, sparse-dense transform unit 200 may transform dense matrices 242, 244, and 246 into one dense matrix for a processor unit. In some implementations, the sparse elements associated with the first dense matrix and the sparse elements associated with the second dense matrix can be multidimensional matrices, and the output dense matrix can be a vector. For example, dense matrix 242 may have dimensions of 100×10, dense matrix 244 may have dimensions of 20×100, and dense matrix 246 may have dimensions of 3×3. Sparse-dense transform unit 200 may transform dense matrices 242, 244, and 246 into one vector having a size of 1x3009. FIG. 5 is a flowchart illustrating an example of a procedure 500 for generating a dense matrix. The procedure 500 may be executed by a system such as the sparse-dense transform unit 104 or the sparse element access unit 300 . The system receives one indication for accessing a particular subset of sparse elements (502). For example, referring to FIG. 3A , data extraction unit 304 may be configured to receive a signal 344 for extracting one or more requested sparse elements from data partition 330 . In some implementations, a request for a particular sparse element stored in one or more data partitions may be received via a network of nodes. For example, referring to FIG. 3A , the request identification unit 302 may be configured to receive a request 342 to fetch a sparse element stored in a data partition 330 via a network of nodes 320 . The system may determine that a data extraction unit is assigned to handle a subset of a particular sparse element. For example, request identification unit 302 may be configured to determine whether sparse element access unit 300 is assigned to access the sparse element indicated by request 342 . In response to determining that the data extraction unit is assigned to handle a particular subset of sparse elements, an indication for accessing the particular subset of sparse elements may be generated. For example, if identification of a particular requested sparse element (e.g., number 1 of database table number 1) is included in a lookup table, request identification unit 302 may extract a signal for the particular requested sparse element 344 sent to the data extraction unit 304. The system determines a processor designation for extracting the particular subset of sparse elements based on the identification of the particular subset of sparse elements (504). For example, referring to FIG. 3A , the data extraction unit 304 includes one or more processors 322a to 322k. Each of the processors 322a-322k can be assigned to a particular sparse element based on the identification of the sparse element, and the data extraction unit 304 can be configured to generate data for one or the other of the processors 322a-322k based on the identification of the sparse element. Multiple requests. In some implementations, the system may determine that the system is assigned to handle a particular subset of sparse elements includes determining that the system is assigned to handle a particular subset of sparse elements based on a lookup table. For example, the data extraction unit 304 can determine the processor assignment by using a lookup table. The system extracts, based on the specification and by a first processor of the plurality of processors, a first sparse element in a subset of the specified sparse elements (506). For example, referring to FIG. 3A , the data extraction unit 304 may instruct the processor 322 a to extract a sparse element included in the signal 344 . The system extracts, based on the specification and by a second processor of the plurality of processors, a second sparse element in a subset of the specified sparse elements (508). For example, referring to FIG. 3A , the data extraction unit 304 can instruct the processor 322b to extract a different sparse element contained in the signal 344 . In some implementations, a first matrix including first sparse elements from a first processor can be received, where the first matrix can have a first size. The system may generate a second matrix including the first sparse elements, the second matrix having a second size smaller than the first size. For example, sparse reduction unit 306 may be configured to reduce the size of extracted sparse elements 346 . Each of processors 322a-322k may generate a sparse element having a size of 100x1. The sparse reduction unit 306 may receive the extracted sparse elements 346 having a size of 100× k , and generate a result by reducing the size of the extracted sparse elements 346 to 100×1 through logical operations, arithmetic operations, or a combination of both. Sparse reduced elements 348. The system can generate an output dense matrix, and the output dense matrix can be generated based on the second matrix. For example, concatenation unit 308 may be configured to reconfigure and concatenate sparsely reduced elements 348 to produce concatenated elements 350 . In some implementations, a first sparse element can be received at a first point in time, and a second sparse element can be received at a second different point in time. The system can determine the order of the first sparse elements and the second sparse elements for outputting the dense matrix. For example, referring to FIG. 3A , the processor 322a may return the extracted sparse element No. 10 to the sparse reduction unit 306 faster than the processor 322b is configured to return the extracted sparse element No. 5. The concatenation unit 308 is configured to reconfigure the later received sparse element No. 5 to be arranged in front of the earlier received sparse element No. 10, and to concatenate the sparse elements Nos. 1 to 200 into the concatenated element 350 . The system generates an output dense matrix based on a transformation applied to at least the first sparse element and the second sparse element (510). In some implementations, the system can compress the output dense matrix to produce a compressed output dense matrix. The system may provide the compressed output dense matrix to a network of nodes. For example, compression/decompression unit 310 may be configured to compress concatenated elements 350 to produce dense matrix 352 for node network 320 . In some implementations, the system may receive a first dense matrix representing a dense matrix sent over the network of nodes, and generate an output dense matrix based on the first dense matrix, the first sparse elements, and the second sparse elements. For example, sparse element access unit 300 may receive a dense matrix from a neighboring sparse element access unit via node network 320 . Sparse element access unit 300 may decompress the received dense matrix and may concatenate the decompressed dense matrix with concatenated elements 350 to form an updated concatenated which may be compressed and then output to node network 320 element. In some implementations, one or more of the particular sparse elements is a multidimensional matrix, and the output dense matrix is a vector. Embodiments of the subject matter and functional operations described in this specification can be implemented in digital electronic circuits, tangibly embodied computer software or firmware, computer hardware, or One or more of them in combination. Embodiments of the subject matter described in this specification may be implemented as one or more computer programs, that is, one or more computer programs encoded on a tangible, non-transitory program carrier for execution by, or to control the operation of, a data processing device. A plurality of computer program instruction modules. Alternatively or additionally, the program instructions may be encoded on an artificially generated propagated signal (e.g., a machine-generated electrical, optical, or electromagnetic signal) that is generated to encode for transmission to Information suitable for receiver means to be executed by a data processing means. The computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of one or more of them. The term "data processing device" includes all kinds of devices, devices and machines for processing data, including by way of example a programmable processor, a computer or a plurality of processors or computers. The device may comprise special purpose logic circuits such as an FPGA (Field Programmable Gate Array) or an ASIC (Application Specific Integrated Circuit). In addition to hardware, the device may also contain code that establishes an execution environment for the computer program in question, for example, constituting processor firmware, a protocol stack, a database management system, an operating system, or the like Code for one or a combination of one or more. A computer program (which may also be called or described as a program, software, a software application, a module, a software module, a script, or code) may be written in any form of programming language (including compiled or interpreted language (or declarative or procedural language), and it may be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment . A computer program may, but need not, correspond to a file in a file system. A program may be stored in a portion of a file that holds other programs or data (for example, in one or more scripts in a markup language document), in a single file dedicated to the program in question, or in In multiple coordination files (for example, files that store one or more modules, subroutines, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network. The procedures and logic flows described in this specification can be executed by one or more programmable computers that execute one or more computer programs to perform by operating on input data and generating output Function. The programs and processes can also be executed by special purpose logic circuits (for example, an FPGA (Field Programmable Gate Array), an ASIC (Application Specific Integrated Circuit) or a GPGPU (General Purpose Graphics Processing Unit)) and the device can also implemented as special purpose logic circuits. Computers suitable for the execution of a computer program include, by way of example, may be based on general or special purpose microprocessors or both or any other kind of central processing unit. Generally, a central processing unit will receive instructions and data from a read only memory or a random access memory or both. The basic elements of a computer are a central processing unit for executing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include or be operatively coupled to receive data from one or more mass storage devices (e.g., magnetic, magneto-optical, or optical disks) for storing data. data or transmit data to it or both receive and transmit data. However, a computer need not have such devices. Additionally, a computer may be embedded in another device such as a mobile phone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a global positioning system (GPS) receiver, to name a few device or a portable storage device (eg, a Universal Serial Bus (USB) flash drive). Computer readable media suitable for storing computer program instructions and data includes all forms of non-volatile memory, media and memory devices, including by way of example: semiconductor memory devices such as EPROM, EEPROM and flash memory devices ; magnetic disks, such as internal hard disks or removable disks; magneto-optical disks; and CD ROM and DVD-ROM disks. The processor and memory can be supplemented by or incorporated in special purpose logic circuitry. To provide for interaction with a user, embodiments of the subject matter described in this specification may be implemented with a display device (for example, a CRT (cathode ray tube) or LCD (liquid crystal display)) for displaying information to the user. monitor) and a keyboard and a pointing device (eg, a mouse or a trackball) on the computer by which the user can provide input to the computer. Other types of devices may also be used to provide interaction with a user; for example, the feedback provided to the user may be any form of sensory feedback, such as visual feedback, auditory feedback, or tactile feedback; and from the User input may be received in any form, including sound, speech, or tactile input. In addition, a computer can interact with a user by sending documents to and receiving documents from a device used by the user; for example, sending web pages in response to requests received from a web browser The page is sent to a web browser on a user's client device. Embodiments of the subject matter described in this specification can be implemented in a computing system that includes a back-end component (for example, as a data server), or that includes an intermediate software component (for example, as an application server server), or include a front-end component (e.g., a client computer having a graphical user interface or a web browser through which a user can interact with an implementation of the subject matter described in this specification) or Any combination of one or more such backend, middleware or frontend components. The components of the system can be interconnected by any form or medium of digital data communication (eg, a communication network). Examples of communication networks include a local area network ("LAN") and a wide area network ("WAN"), such as the Internet. The computing system may include clients and servers. A client and server are generally remote from each other and usually interact through a communication network. The relationship of client and server arises by means of computer programs running on the respective computers and having a client-server relationship to each other. While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any invention or of what may be claimed, but rather as illustrations of features that may be specific to particular embodiments of particular inventions. . Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Furthermore, while features above may be stated as functioning in particular combinations, and even initially claimed as such, in some cases one or more features from a claimed combination may be removed from that combination and the claimed A combination may be directed to a sub-combination or a variation of a sub-combination. Similarly, while operations are depicted in a particular order in the drawings, this should not be understood as requiring that such operations be performed in the particular order shown, or in sequential order, or that all illustrated operations be performed, to achieve the desired result. In certain circumstances, multitasking and parallel processing may be advantageous. Furthermore, the separation of the various system modules and components in the embodiments described above should not be construed as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in within a single software product or packaged into multiple software products. Specific embodiments of the subject matter have been described. Other embodiments are also within the scope of the following claims. For example, the actions recited in the claims can be performed in a different order and still achieve desirable results. As one example, the procedures depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In particular implementations, multitasking and parallel processing may be advantageous.

100: computing system 102: processing unit 104: sparse-dense transformation unit 106a-106k: data partition 108a-108n: sparse element 110: instruction 112: target dense matrix 200: sparse-dense transformation unit 202: first column 204: first row Second column 206: M column 222: request 224: request 226: request 230: request 242: dense matrix 244: dense matrix 246: dense matrix 252: sparse element update request 254: sparse element update request 256: request 260: request 300 : sparse element access unit 302: request identification unit 304: data extraction unit 306: sparse reduction unit 308: concatenation unit 310: compression/decompression unit 312: split unit 320: node network 322a-322k: processor 330: Data Partition 342: Request/Broadcast Request 344: Signal 346: Extracted Sparse Elements 348: Sparsely Reduced Elements 350: Concatenated Elements 352: Dense Matrix 362: Request 364: Indicates X _1,1 -X _M,N : Sparse element access unit

FIG. 1 is a block diagram of an exemplary computing system. 2A-2D illustrate an example sparse-dense transform unit. 3A-3B illustrate an example sparse element access unit. Figure 4 is a flowchart illustrating an example of a procedure for generating a dense matrix. Figure 5 is a flowchart illustrating an example of a procedure for transforming sparse elements into a dense matrix. In the various drawings, like element symbols and names indicate like elements.

100: Computing Systems

102: Processing unit

104:Sparse-dense transformation unit

106a-106k: data partition

108a-108n: sparse elements

110: instruction

112: Target Dense Matrix

Claims (15)

A system for transforming sparse (sparse) elements into a dense (dense) matrix, the system comprising: a plurality of sparse element access units, each sparse element access unit of the plurality of sparse element access units is grouped state to: receive respective control signals; access a plurality of sparse elements stored in a data partition (shard) corresponding to the sparse element access unit based on the respective control signals; transforming one of the obtained sparse elements to generate an output dense matrix; and providing the output dense matrix to a network of nodes of the system. The system of claim 1, further comprising: a sparse-dense transformation unit configured to receive instructions corresponding to the respective control signals, wherein the plurality of sparse element access units are located in the sparse-dense in the transformation unit. The system according to claim 2, wherein the sparse-dense transformation unit includes a multi-dimensional sparse-dense transformation unit of a row dimension and a column dimension. The system of claim 3, wherein the plurality of sparse element access units are arranged along respective dimensions of the multi-dimensional sparse-dense transformation unit. The system of claim 2, wherein each of the plurality of sparse element access units: comprises a respective first unit configured to apply the transformation to the sparse elements to generate the output dense matrix. The system of claim 5, wherein: the first unit is a concatenation unit; and the transformation is based on a concatenation operation. The system of claim 5, wherein: the first unit is a compression/decompression unit; and the transformation is based on an operation of compressing the sparse elements. A method for transforming sparse elements into a dense matrix using a system comprising a plurality of sparse element access units, the method comprising: receiving respective control signals by a sparse element access unit; by the sparse an element access unit accesses a plurality of sparse elements stored in a data partition corresponding to the sparse element access unit based on the received respective control signals; transforming one of the elements to generate an output dense matrix; and providing the output dense matrix to a network of nodes of the system. The method as claimed in item 8, wherein: The system includes a sparse-dense transform unit configured to receive instructions; the plurality of sparse element access units are located in the sparse-dense transform unit; and the method includes receiving, by the sparse-dense transform unit, corresponding Instructions for respective control signals at each of the plurality of sparse element access units. The method of claim 9, wherein the sparse-dense transformation unit is a multi-dimensional sparse-dense transformation unit comprising a column dimension and a row dimension. The method of claim 10, wherein the plurality of sparse element access units are arranged along respective dimensions of the multi-dimensional sparse-dense transformation unit. The method of claim 9, wherein: each of the plurality of sparse element access units includes a respective first unit configured to transform the sparse elements; and the method includes, by the first unit The transformation is applied to the sparse elements to produce the output dense matrix. The method of claim 12, wherein: the first unit is a concatenated unit; and applying the transformation comprises: applying a concatenation operation to the sparse elements; and concatenating the sparse elements based on the concatenation operation to generate This outputs a dense matrix. The method of claim 12, wherein: the first unit is a compression/decompression unit; and applying the transformation comprises: applying a compression operation to the sparse elements; and compressing the sparse elements based on the compression operation to generate the output a dense matrix. A non-transitory machine-readable storage device storing instructions for transforming sparse elements into a dense matrix by a plurality of sparse element access units of a system, the instructions being executable by a processor to cause Including the performance of: receiving respective control signals by a sparse element access unit; accessing, by the sparse element access unit, data stored corresponding to the sparse element access unit based on the respective control signals a plurality of sparse elements in a partition; generating an output dense matrix based on a transformation applied by the sparse element access unit to the sparse elements obtained from the data partition; and providing the output dense matrix to the system One node network.

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